Wednesday, April 13, 2016

Opposite Pi Day (Day 139)

Today I subbed in a seventh grade math class. Unlike last week's math class that was still somehow still in Chapter 2, this class was paced much more reasonably. The students finished the Chapter 7 test yesterday, and so they are ready to begin Chapter 8 today.

Last week, I wrote that Chapter 8 of my district's seventh grade text is "Measure Figures." I also wrote last week that seventh grade is the year when students learn how to measure circles:

CCSS.MATH.CONTENT.7.G.B.4
Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle.

And we all know what this means -- today was the day the students begin learning about pi!

Of course I am posting today's worksheet on the blog. For this activity, the students are given four round objects and a tape measure, and they are to measure the circumference and diameter of each of the objects. For example, one of the objects is a heart tin -- its circumference is about 47 cm and its diameter is about 15 cm.

You may notice that there's room to measure five objects, not just four. Well, the fifth object is the circle painted on the outdoor basketball court. This is convenient because its diameter is already marked (the free-throw line). But the students, instead of bringing the tape measure outside, use a nonstandard unit to measure the circle -- their own feet. With basketball on the mind of so many Californians today -- here in the south we celebrate Kobe Bryant's final game, while those in the north hope the Warriors win their 73rd game today -- it's great to incorporate the sport into today's lesson.

Notice that students are not to fill out the column "What relationship do you see?" yet. But some students try to come up with a relationship anyway. One student tries subtracting the diameter from the circumference, to write something like, "The circumference is 32 cm more than the diameter." I argue that this student is actually on the right track, if you think about it.

Meanwhile, a few students have already heard of pi, so they already know the relationship. One student cheats by measuring the diameters and simply multiplying each one by 3.14. The regular teacher will probably reveal the relationship between the circumference and diameter tomorrow.

Most of the students enjoy the lesson, but a few wonder why we are doing this activity. But most likely, these students are upset because they finish measuring the basketball court before any other group and is hoping for a reward. Instead, they are caught by another teacher for attempting to return to the classroom and fool around while I'm still out watching the other students.

Let's think about where this lesson fits in the seventh grade curriculum. Last week I wrote that if I were teaching the class, I'd try to reach Chapter 8 by Pi Day. As we see, this class came close -- certainly much closer than last week's Chapter 2 class.

But it can be argued that today is actually a "Pi Day" of sorts. You see, instead of 3/14, today is April 13th, which is 4/13. As the digits of pi appear in reverse, we can think of this as "Opposite Pi Day."

And now you're thinking -- here we go grasping at straws to come up with another math holiday. We already have Pi Day on March 14th, Pi Approximation Day on July 22nd, and Pumpkin Pi Day on the 314th day of the year in November. We had Square Root Day of the Decade on 4/4/16, Square Root Day of the Century on 4/5/2025, and several Square Root Days of the Month -- including yesterday, April 12th, which can serve as sqrt(17) day. And now I insist on adding yet another Pi Day on April 13th just because 3/14 reversed is 4/13! Do I really think that anyone is actually going to celebrate any of these extra so-called "Pi Days"?

Well, actually I didn't invent "Opposite Pi Day" -- the creator of the following video did:

It's yet another parody of Rebecca Black's "Friday" -- as I mentioned back on the original Pi Day, the fact that Friday and Pi Day rhyme is too irresistible for many math parodists to avoid. The poster of this song, who goes by the username "AsianGlow," probably just missed uploading the song on the original Pi Day, so rather than wait a whole year to post it, he just reversed the digits. He uploaded the video exactly five years ago today -- April 13th, 2011.

AsianGlow writes:

Of course by now you know of Rebecca Black making her infamous debut with Friday, but what about Pi Day?

How come Fridays get so much more love? Friday usually gets four times a month to party, but Pi Day only gets one... March 14th...

Does this mean I can only eat pies once a year?! OMG NO! Any date containing 1, 3, or 4 should be a piece of Pi Day! hahaha! See what I did there? You don't think it's funny? Well don't be so bitter and get some sweets in yo life! :D

This is the first video in a while that I did allll by myself! Well the filming anyways...
FilmRebelRoby - http://youtube.com/filmrebelroby - helped me with mastering my vocals.

April 13 is like opposite Pi Day! OMG it's still April fools! That's right, that's Pi!

Notice that AsianGlow's proposal that any date containing 1, 3, and 4 should be Pi Day only applies to March 14th and April 13th. We see that January 34th, April 31st, and 13/4 all just barely avoid being valid Gregorian dates, but they could exist in certain versions of Calendar Reform. In particular, all three date exist in a Leap Week Calendar where every third month (including January and April) have 35 days, 28 days in all the rest, and Leap Week labeled as Month 13.

I wouldn't have mentioned Opposite Pi Day here on the blog at all had I not subbed in a class learning about pi today. In some ways, I'm celebrating Opposite Pi Day today for the exact same reason as AsianGlow -- we both already missed the real Pi Day, yet we want to celebrate pi today. Both Pi Day and Square Root Day can be easily manipulated so that they fall during the unit on pi or square roots.

Meanwhile, how does today's pi lesson fit into our lesson plans for the blog? Well, we're currently in a unit on circles and spheres, so pi naturally fits with that. Dr. Franklin Mason actually includes pi in the same chapter as the Inscribed Angle Theorem, in his Chapter 9 on circles. Pi is covered in his Lesson 9.3, while the Inscribed Angle Theorem is Lesson 9.5. Other texts, like the U of Chicago text, separate pi from the circle theorems. So pi appears in our Lesson 8-8, far away from the Inscribed Angle Theorem in Lesson 15-3.

Though officially I covered pi on the blog on the original Pi Day -- and that includes both the circumference and area formulas -- the actual lesson focused more on area. This follows the lesson plans on Dr. Hung-Hsi Wu. Yes, I gave circumference first, but the area activity is Wu's. Today I finally post a lesson where students experiment with circumference. Of course, with these two lessons a week apart, the last part of that Common Core Standard:

CCSS.MATH.CONTENT.7.G.B.4
...give an informal derivation of the relationship between the circumference and area of a circle.

isn't fully emphasized here on the blog. I alluded to this derivation in yesterday's post, when I was discussing Archimedes and his "cut-and-roll formula." I mention cut-and-roll on the blog, but not on any student worksheet.

Also, it's logically possible to include area in the area unit (Chapter 8) and circumference in the current unit (circles/Chapter 15), since Wu teaches area of a circle before circumference. Of course, if we were really doing this, we should have covered circumference before yesterday's Isoperimetric Theorem, which mentions circumference throughout this lesson. Also, it makes sense to teach circumference before surface area and volume in Chapter 10.

Still, this is a nice activity to include in the current unit. Here is the worksheet: